Weingast B.R., Wittman D. The Oxford Handbook of Political Economy

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902 economic methods in political theory

as a tool for political science. Things changed with the development of techniques

within economics and game theory that greatly extended the scope and power of non-

cooperative game theory, in which there is no presumption that the existence of gains

from cooperation are realized. And at least at the time of writing this chapter, it is

non-cooperative game theory that dominates contemporary positive political theory.

This chapter concerns economic methods in political science. It is conﬁned ex-

clusively to positive (formal) political theory, paying no attention to econometric

methods for empirical political science. Furthermore, I adopt the perspective that

a central task for positive political theory is to understand the relationship between

the preferences of individuals comprising a polity and the collective choices from a

set of possible alternatives over which the individuals’ preferences are deﬁned.

The

next section sketches the two canonical approaches to developing a positive political

theory, collective preference theory and game theory. I brieﬂy argue that despite some

clear formal diﬀerences, these two techniques are essentially distinguished by the

trade-oﬀ each makes with respect to a minimal democracy constraint and a demand

that well-deﬁned predictions are generally guaranteed. Moreover, the attempt to

develop collective preference theory as an explanatory framework for political science

reveals two important analytical characteristics, distinctive to political science rather

than economics. The subsequent section, therefore, considers some more speciﬁc

techniques within the game-theoretic approach designed to accommodate these char-

acteristics. A third section concludes.

2 Two Approaches From Economics

.............................................................................

Economics is rooted in the choices of individuals, albeit with a broad notion of what

counts as an “individual” when useful, as in the theory of markets where ﬁrms are

often treated as individuals. And the basic economic model of individual choice is

decision theoretic: in its simplest variant, individuals are assumed to have preferences

over a set of feasible alternatives that are complete (every pair of alternatives can be

ranked) and transitive (for any three alternatives, say x, y, z,ifx is preferred to y

and y is preferred to z,thenx must be preferred to z) and to choose an alternative

(e.g.purchasingbundlesofgroceries,cars,education,...)thatmaximizestheirpref-

erences, or payoﬀs, over this set. The predictions of the model, therefore, are given

⁴ Of course, this understanding itself reﬂects a largely consequentialist perspective intrinsic to

economics. Insofar as there is consideration with any economic process, it is rarely with the process per

se but with respect to the outcomes supported or induced by that process. This remains true for

normative analysis. For example, axiomatic characterizations of procedures for dispute resolution (such

as bargaining or bankruptcy) rarely exclude all references to the consequences of using such procedures:

Pareto eﬃciency and individual rationality are common instances of such consequentialist properties. In

contrast, a consequentialist perspective is less well accepted within political science at large, where (inter

alia) there is widespread concern with, say, the legitimacy of procedures independent of the outcomes

they might induce.

david austen-smith 903

by studying how the set of maximal elements varies with changes in the feasible set.

Now it is certainly true that individuals make political decisions but those decisions of

interest to political science are not primarily individual consumption or investment

decisions; rather, they are decisions to vote, to participate in collective action, to adopt

a platform on which to run for elected oﬃce, and so forth. In contrast to canonical

decision-making in economics, therefore, what an individual chooses in politics is not

always what an individual obtains (e.g. voting for some electoral candidate does not

ensure that the candidate is elected). Thus, the link between an individual’s decisions

in politics and the consequent payoﬀs to the individual is attenuated relative to

that for economic decisions: the basic political model of individual choice is game

theoretic.

The preceding observations suggest two approaches to understanding how indi-

vidual preferences connect to political, or collective, choices and both are pursued: a

direct approach through extending the individual decision-theoretic model to the col-

lectivity as a whole, an approach essentially begun with Arrow (1951, 1963)andBlack

(1958); and an indirect approach through exploring the consequences of mutually

consistent sets of strategic decisions by instrumentally rational agents, an approach

with roots in von Neumann and Morgenstern (1944) and Nash (1951).

Under the direct (collective preference) approach to social choice, individuals’

preferences are directly aggregated into a “social preference” which, as in individual

decision theory, is then maximized to yield a set of best (relative to the maximand)

alternatives, the collective choices. But although individual preferences surely in-

ﬂuence individual decisions such as voting, there is no guarantee that individuals’

preferences are revealed by their decisions (for example, an individual may have strict

preferences over candidates for electoral oﬃce, yet choose to vote strategically or to

abstain). Under the indirect (game-theoretic) approach to social choice, therefore, it

is individuals’ actions that are aggregated to arrive at collective choices. Faced with

a particular decision problem, individuals rarely have to declare their preferences

directly but instead have to take some action. For example, in a multicandidate

election under plurality rule, individuals must choose the candidate for whom to vote

and may abstain; the collective choice from the election is then decided by counting

the recorded votes and not by direct observation of all individuals’ preferences over

the entire list of candidates. It is useful to be a little more precise.

A preference proﬁle is a list of preferences, one for each individual in the society,

over a set of alternatives for that society. An abstract collective choice rule is a rule that

assigns collective choices to each and every proﬁle; that is, for any list of preferences,

a collective choice rule identiﬁes the set of outcomes chosen by society. Similarly,

a preference aggregation rule is a rule that aggregates individuals’ preferences into

a single, complete, “social preference” relation over the set of alternatives; that is, for

any proﬁle, the preference aggregation rule collects individual preferences into a social

preference relation over alternatives. It is important to note that while the theory

(following economics) presumes individual preferences are complete and transitive,

the only requirement at this point of a social preference relation is that it is complete.

For any proﬁle and preference aggregation rule, we can identify those alternatives (if

904 economic methods in political theory

any) that are ranked best by the social preference relation derived from the proﬁle

by the rule. With a slight abuse of the language, this set is known as the core of

the preference aggregation rule at the particular proﬁle of concern.

Ta ken t og et he r,

therefore, a preference aggregation rule and its associated core for all possible prefer-

ence proﬁles is an instance of an abstract collective choice rule. Thus, the extension of

the classical economic decision-theoretic model of individual choice to the problem

of collective decision-making, the direct approach mentioned above, can be described

as the analysis of the abstract collective choice rules deﬁned by the core of various

preference aggregation rules.

The analytical challenge confronted by the direct approach is to ﬁnd conditions un-

der which preference aggregation relations exist and yield well-deﬁned, that is, non-

empty, cores. This approach has focused on two complementary issues: delineating

classes of preference aggregation rule that are consistent with various sets of desiderata

(for instance, Arrow’s possibility theorem (1951, 1963) and May’s theorem (May 1952)

characterizing majority rule) and describing the properties of particular preference

aggregation rules in various environments

(for instance, Plott’s characterization of

majority cores (Plott 1967) in the spatial model and the chaos theorems of McKelvey

1976 1979,andSchoﬁeld1978, 1983). Contributions to the ﬁrst issue rely heavily on

axiomatic methods whereas contributions to the second have, for the most part,

exploited the spatial voting model in which the feasible set of alternatives is some

subset of (typically) k-dimensional Euclidean space and individuals’ preferences can

be described by continuous quasi-concave (loosely, single peaked in every direction)

utility functions.

From the perspective of developing a decision-theoretic approach to prediction

and explanation at the collective level, the results from collective preference theory

are a little disappointing. There exist aggregation rules that justify treating collective

choice in a straightforward decision-theoretic way only if the environment is very

simple, having a minimal number of alternatives from which to choose or satisfying

severe restrictions on the sorts of preference proﬁles that can exist (for instance,

proﬁles of single-peaked preferences over a ﬁxed ordering of the alternatives), or

if the preferences of all but a very few are ignored in the aggregation (as in dic-

tatorships). Moreover, in the context of the spatial model, most of the aggregation

procedures observed in the world are, at least in principle, subject to chronic in-

stability unless politics concerns only a single issue.

Nevertheless, a great deal has

been learned from the collective preference approach to political decision-making

about the properties and implications of preference aggregation and voting rules,

⁵ The abuse arises since, strictly speaking, the core is deﬁned with respect to a given family of

coalitions. To the extent that a preference aggregation rule can be deﬁned in terms of so-called decisive,

or winning coalitions, the use of the term is standard. But not all rules can be so deﬁned in which case

the set of best elements induced by such a rule is not a core in the strict sense (see, for example,

Austen-Smith and Banks 1999,ch.3). The terminology in these instances is therefore an abuse but a

useful and harmless one nevertheless.

⁶ That is, various admissible classes of preference proﬁles and sorts of feasible sets of alternatives.

⁷ See Austen-Smith and Banks 1999 for an elaboration of these claims.

david austen-smith 905

and about the normative and descriptive trade-oﬀs inherent in choosing one rule

over another.

Unlike the direct collective preference approach, the indirect approach to collective

choice through the aggregation of the strategic decisions of instrumentally rational

individuals begins by specifying the collection of possible decision, or strategy, pro-

ﬁles that could arise. A strategy for an individual speciﬁes what the individual would

do in every possible contingency that could arise in the given setting. A strategy

proﬁle is then a list of individual strategies, one for each member of the polity. An

outcome function is a rule that identiﬁes a unique alternative in the set of possible

social alternatives with every feasible strategy proﬁle. A speciﬁcation of all possible

strategy proﬁles along with an outcome function is called a mechanism.Anabstract

theory of how individuals make their respective decisions under any mechanism is

a rule that associates a strategy proﬁle with every preference proﬁle; that is, for any

given preference proﬁle, an abstract decision theory assigns a set of possible strategy

proﬁles consistent with the theory when individuals’ preferences are described by

the given list of preferences.

For any preference proﬁle, mechanism, and decision

theory, we can identify those alternatives that could arise as outcomes from strategy

proﬁles consistent with the decision theory at that preference proﬁle. This is the

set of equilibrium outcomes under the mechanism at the preference proﬁle. Then

the indirect approach to preference aggregation can be described as the analysis of

the collective choice rules deﬁned by the sets of equilibrium outcomes of various

mechanisms and theories of individual decision-making.

There is no eﬀort under the indirect approach to treat collective decision-making

as in any way analogous to individual decision-making. Instead, individuals make

choices (vote, contribute to collective action, and so forth) taking account of the

choices of others and the likely consequences of various combinations of the individ-

uals’ decisions. Although such choices are expected to reﬂect individual preferences,

there is no presumption that they do so in any immediately transparent or literal

fashion. The approach therefore requires both a theory of how individuals make

their decisions (the abstract theory of decision-making considered above) and a

description of how the resulting decisions are mapped into collective choices (a spec-

iﬁcation of the outcome function). Putting these two components together with pref-

erences then yields a model of collective choice through the aggregation of individual

decisions.

Unlike the collective preference approach, there is little diﬃculty with developing

coherent predictive models of collective choice within the game-theoretic framework.

That is, while the social choice mapping derived from a preference aggregation rule

rarely yields maximal elements, the mapping derived from a mechanism and theory

of individual behavior is typically well deﬁned. This fact, coupled with the ﬂexibility

⁸ It is worth pointing out here, too, that the typical emptiness of the core has stimulated work on

solutions concepts other than the core for collective preference theory (e.g. Schwarz 1972;Miller1980;

McKelvey 1986).

⁹ Examples of such decision theories include Nash equilibrium and its reﬁnements. See Fudenberg

and Tirole 1991 or Myerson 1991.

906 economic methods in political theory

of the approach with respect to modeling institutional details, uncertainty, and in-

complete information, has led to game theory dominating contemporary formal the-

ory. Indeed, it has been argued that the adoption of (in particular) non-cooperative

game-theoretic techniques represents a fundamental shift in methodology from those

of collective preference theory (e.g. Baron 1994;Diermeier1997). Yet, at least from a

formal perspective, the diﬀerence between the collective preference and the game-

theoretic approaches is not so stark.

Both approaches to collective choice, the direct and the indirect, yield social choice

rules, taking preference proﬁles into collective choices. Thus any result concerning

such rules must apply equally to both. In particular, it is true that a social choice

rule is generally guaranteed to yield a non-empty core only if it violates a “minimal

democracy” property, where “minimal democracy” means that if all but at most

one individuals strictly prefer some alternative x to another y,theny should not

be ranked strictly better than x under the choice rule (Austen-Smith and Banks

1998). Whence it follows that the indirect approach ensures existence of well-deﬁned

solutions by violating minimal democracy, whereas the direct approach insists on

minimal democracy at the expense of ensuring non-empty cores in any but the

simplest settings. On this account, the direct and the indirect approaches to un-

derstanding collective decision-making are complementary rather than competitive.

Which sort of model is most appropriate depends on the problem at hand and, in

some important cases, their respective predictions are intimately related (Austen-

Smith and Banks 1998, 2004). Moreover, the collective preference approach has re-

vealed two general analytical characteristics of collective decision-making peculiar to

political science relative to economics, characteristics that have stimulated important

methodological and substantive innovations in the game-theoretic approach. It is to

these characteristics and the innovations they have induced that I now turn.

3 Two Analytical Characteristics

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The ﬁrst characteristic exposed by collective preference theory involves the role of

opportunities for trade. In economics, it is typically the case that, for any given

society, the greater are the opportunities for trade the more likely it is that welfare-

improving trade takes place. The analogue to increasing opportunities for trade in

politics is increasing the dimensionality of the policy space in the spatial model or the

number of alternatives in the ﬁnite-alternative model. As the number of alternatives

or issue dimensions on which the preferences of a given population can diﬀer grows,

so too does the number of opportunities for winning coalitions to agree on a change

from any policy; with one dimension, for example, coalitions must agree either to

“move policy to the left” or to “move policy to the right” but, with two dimensions,

there are uncountable directions in which to change policy, and preferences can be

distributed over the plane, permitting more coalitions to form against any given

david austen-smith 907

policy. But it is precisely in such complex settings that preference aggregation rules are

most poorly behaved: with one dimension the median voter theorem ensures a well-

deﬁned collective choice under majority rule (Black 1958) but, with two dimensions,

the existence of such a choice is an extremely rare event and virtually any pair of alter-

natives can be connected by a ﬁnite sequence of majority-preferred steps (McKelvey

1979). Thus increasing “opportunities for trade” in the political setting exacerbate the

problems of reaching a collective choice rather than ameliorate them.

The second characteristic concerns large populations. In economics it is the market

that aggregates individual decisions into a collective outcome. As the number of

individuals grows, the inﬂuence of any single agent becomes negligible and, in the

limit, instrumentally rational individuals act as price-takers; moreover, large pop-

ulations tend to smooth over non-convexities and irregularities at the individual

level, justifying an approximation that all members of the population act as canonic

economic theory presumes. These nice properties do not hold in political settings.

Individual decisions are aggregated through voting and although the likelihood that

any individual is pivotal vanishes as the electorate grows, for any ﬁnite society that

likelihood is not zero: under majority rule in the classical Downsian spatial model,

the median voter is pivotal whether there are three voters or three billion and three.

So not only can the collective choice depend critically on a single person’s decision, it

is unjustiﬁed to treat each agent analogously to a “price-taker” and non-convexities

and irregularities can matter a great deal depending on precisely where they are

located in the population. The “correct” model of decision-making here is therefore

to presume individuals condition their choices on being pivotal and act as if their

vote or contribution or whatever tips the balance in favour of one or other collective

choice: either they are not in fact pivotal in which case their decision is irrelevant, or

they are pivotal in which case their decision determines the collective choice.

The conclusion that rational individuals condition their vote decisions on the event

that they are pivotal is a strategic, game-theoretic, perspective and it is within this

framework that eﬀorts to tackle the problems raised by each characteristic have been

undertaken.

3.1 Institutions and Explanation

A virtue of the collective preference methodology (and, to a large extent, the coop-

erative game-theoretic methodology exploited by Riker 1962 and others) is that it is

essentially “institution free,” focusing exclusively on how domains of preference pro-

ﬁles are mapped into collective choices without attention to how the proﬁles might be

recorded, from where the alternatives might arise, and so on. The idea underlying the

axiomatic method of collective preference theory is to abstract from empirical and

¹⁰ While this applies to any large ﬁnite electorate, proceeding to the limit in which each voter is

inﬁnitessimally small removes even this prescription regarding how strategically rational agents may

behave, on which more below.

908 economic methods in political theory

detailed institutional complications and study whole classes of possible institution-

satisfying particular properties. A limitation of this method for an explanatory theory,

however, is the typical emptiness of the core in complex settings, that is, those with

many issues or alternatives over which to choose. And although non-cooperative

game theory typically requires an exhaustive description of the relevant institutional

details in any application, it is rarely hampered by questions of the existence of

solutions. This observation prompted a shift in emphasis away from a collective

preference methodology tailored to avoid concerns with the details of any application,

to a non-cooperative game-theoretic approach that embraces such details as intrinsic

to the analysis.

Two illustrations of the role of institutional detail in ﬁnessing problems of existence

in complex political environments are provided by the use of particular sorts of

agenda in committee decision-making from ﬁnite sets of alternatives (see Miller 1995

for an overview) and the citizen-candidate approach to electoral competition in the

spatial model, whereby the candidates contesting an election are themselves voters

whostrategicallychoosewhetherornottorunforoﬃce at some cost (Osborne and

Slivinsky 1996;BesleyandCoate1997).

In the classical preference proﬁle to illustrate the instability of majority rule (the

Condorcet paradox), three committee members have strict preferences over three

alternatives such that each alternative is best in one person’s ordering, middle ranked

in a second person’s ordering, and worst in a third person’s ordering. There is no

majority core in this example, with every alternative being beaten by one of the others

under majority preference. However, committee decisions are often governed by rules,

such as the amendment agenda. Under the amendment agenda, one alternative is

ﬁrst voted against another and the majority winner of the vote (not preference) is

then put against the residual alternative in a ﬁnal majority vote to determine the

outcome. It is well known that the unique subgame perfect Nash equilibrium (an

instance of a theory of individual decision-making in the earlier language) prescribes

that individuals vote with their immediate (sincere) preferences at the ﬁnal division

to yield two conditional outcomes, one for each possible winner at the ﬁrst division,

and then vote sincerely at the ﬁrst division with respect to these two conditional

outcomes. Assuming majority preference is always strict, this backwards induction

procedure invariably produces a unique prediction which in general depends on the

ordering of the alternatives as well as the distribution of individual preferences per

se.

Moreover, the set of possible outcomes from amendment agendas (on any given

ﬁnite set of alternatives and any ﬁnite committee) as a function of the preference

proﬁles inducing a strict majority preference relation is now completely characterized

(Banks 1985).

Similar to the diﬃculty with many alternatives illustrated by the Condorcet para-

dox, the majority rule core in the multidimensional spatial model is typically empty,

and core emptiness means the model oﬀers no positive predictions beyond the claim

¹¹ It is worth noting in this example that the equilibrium outcome surely violates minimal

democracy because, for every possible decision, there is an alternative that is strictly preferred by two of

the three individuals.

david austen-smith 909

that for every policy, there exists an alternative policy and a majority that strictly

prefers that alternative. But policies are oﬀered by candidates and candidates are

themselves members of the electorate. It is natural, therefore, to treat the set of

potential candidates as being exactly the set of citizens. Furthermore, since citizens are

endowed with policy preferences, other things equal and conditional on being elected,

a successful candidate has no incentive to implement any platform other than his or

her most preferred policy. In turn, rational voters recognize that whatever a candidate

drawn from the electorate might promise in the campaign, should the candidate be

elected then that person’s ideal policy is the ﬁnal outcome. When the set of potential

candidates coincides with the set of voters, therefore, there is no essential diﬀerence

between the problem of electoral platform selection and the problem of candidate en-

try: explaining the distribution of electoral policy platforms in the citizen-candidate

model is equivalent to explaining the distribution of citizens who choose to run for

electoral oﬃce. And assuming that it is costly to run for oﬃce, individuals weigh

the expected gains (which depend, inter alia, on who else is running) from entering

an election against this cost when deciding whether to run for oﬃce. It follows that

alternatives are costly to place on the agenda in the citizen-candidate model and it is

not hard to see, then, that these institutional details introduce suﬃcient stickiness to

ensure the existence of equilibria. Moreover, by varying parameters such as the cost

of entry, the electoral rule of concern, and so forth, various comparative predictions

concerning policy outcomes and electoral system are available.

3.2 Information and Large Populations

Beyond questions of core existence, the application of the collective preference model

to environments in which individuals face considerable uncertainty, either about the

implications of any collective decision (imperfect information) or about the prefer-

ences of others (incomplete information), is awkward. Non-cooperative game theory,

however, can readily accommodate uncertainty and informational variations.

And

whereas uncertainty is unnecessary for developing a coherent theory of economic

behavior among large populations (in particular, the theory of perfect competition),

it is uncertainty that provides a hook on which to develop a coherent theory of

political behavior among large populations.

As remarked above, a peculiarity of political decision-making relative to economic

decision-making is that consideration of large populations greatly complicates rather

than simpliﬁes the analysis of individual decisions. In markets, each consumer be-

comes negligible with respect to inﬂuencing price as the number of consumers grows

¹² The contemporary literature on game-theoretic models of comparative institutions is large and

growing. Examples include Austen-Smith and Banks 1988;Cox1990; Persson, Roland, and Tabellini 1997;

Myerson 1999; and Diermeier, Eraslan, and Merlo 2003.

¹³ The theoretical foundations were laid by Harsanyi 1967–8. Two particularly important papers since

then for political science are Spence 1973, who introduced the class of signaling games, and Crawford

and Sobel 1982, who extended this class to include cheap-talk (costless) signaling.

910 economic methods in political theory

and, therefore, is properly conceived as taking prices as given; in electorates, however,

while it remains true that the likelihood that any single vote tips the outcome becomes

vanishingly small as the number of voters grows, it is not true (at least for ﬁnite

electorates) that the behavior of any given voter should be conditioned on the almost

sure event that the voter’s decision is consequentially irrelevant. This is not usually a

problem for classical collective preference theory which, as the name suggests, focuses

on aggregating given preference proﬁles, not vote proﬁles. Nor is it any problem for

Nash equilibrium theory insofar as there are a huge number of equilibrium patterns

of voting in any large election (other than with unanimity rule), most of which look

empirically silly. But empirical voting patterns are not arbitrary. And once account is

taken of the fact that preferring one candidate to another in an election does not imply

voting for that candidate (individuals can abstain or vote strategically), there is clearly

a severe methodological problem with respect to analysing equilibrium behavior in

large electorates.

One line of attack has been by brute force, using combinatorial techniques to

compute the probability that a particular vote is pivotal, conditional on the speciﬁed

(undominated) votes of others (Ledyard 1984;Cox1994; Palfrey 1989). But this is

cumbersome and places considerable demands on exactly what it is that individuals

know about the behavior of others. In particular, individuals are assumed to know

the exact size of the population. Myerson (1998, 2000, 2002) relaxes this assumption

and develops a novel theory of Poisson games to analyse strategic behavior in large

populations.

Rather than assume the size of the electorate is known, suppose that the actual

number of potential voters is a random variable distributed according to a Poisson

distribution with mean n,wheren is large. Then the probability that there is any

particular number of voters in the society is easily calculated. As a statistical model

underlying the true size of any electorate, the Poisson distribution uniquely exhibits

a very useful technical property, environmental equivalence: under the Poisson distri-

bution, any individual in the realized electorate believes that the number of other

individuals in the electorate is also a random variable distributed according to a

Poisson distribution with the same mean. And because the number and identity of

realized individuals in the electorate is a random variable, it is enough to identify

voters by type rather than their names, where an individual’s type describes all of the

strategically relevant characteristics of the individual (for example the individual’s

preferences over the candidates seeking oﬃce in any election). If the list of possible

individual types is ﬁxed and known, then the distribution of each type in a realized

population of any size is itself given by a Poisson distribution.

The preceding implications of modeling population size as an unobserved draw

from a Poisson distribution allow a relatively tractable and appealing strategic theory

of elections. Because only types are relevant, individual strategies are appropriately

deﬁned as depending only on voter type rather than on voter identity. Thus individ-

uals know only their own types, the distribution of possible types in the population,

that the population size is a random draw from a Poisson distribution, and that all

individuals of the same type behave in the same way. Call such a strategic model a

david austen-smith 911

Poisson game. An equilibrium to a Poisson game is then a speciﬁcation of strategies,

one for each type, such that, for any individual of any type, the individual is taking

a best decision taking as given the strategies of all other types, conditional on his

or her beliefs regarding the numbers of individuals of each type in the electorate.

Such equilibria exist and have well-deﬁned limits with strictly positive turnout as

the mean population size increases. Myerson proposes using these limiting equilibria

as the basis of predictions about political behavior in large populations. And to

illustrate the relative elegance of the method over the usual combinatoric approach,

in Myerson (2000) he provides a version of a theorem on turnout and candidate

platform convergence due to Ledyard (1984) and, in Myerson (1998), he establishes

a Condorcet jury theorem (see also Myerson 2002 for a comparative analysis of three-

candidate elections under scoring rules using a Poisson game framework).

In economics, markets also serve to aggregate information through relative prices.

There are no relative prices explicit in elections, yet it is not only implausible to

presume voters know the true size of the electorate, it is also implausible that they

know the full implications of electing one candidate rather than another. Because the

likelihood that any single vote is pivotal in a large election is negligible, the incentives

for any one voter in a large electorate to invest in becoming better informed regarding

the candidates for election are likewise negligible. Thus Downs (1957) argued that

voters in large populations would be “rationally ignorant.” But just as is the case

with his theory of participation, Downs’s argument is decision-theoretic and does

not necessarily apply once the strategic character of political behavior is made

explicit. In particular, an instrumentally rational voter conditions her vote on the

event that she is pivotal; and in the presence of asymmetric information throughout

the electorate, conditioning on the event of being pivotal can yield a great deal of

information about what others know. To see this, consider an example in which two

candidates are competing for a majority of votes in a three-person electorate. Suppose

each voter receives a noisy private signal correlated with which of the two candidates

would be best and (for simplicity) suppose further that all voters share identical full-

information preferences. Now if the ﬁrst two voters are voting sincerely relative to

their signals and the third voter is pivotal, it must be the case that the ﬁrst two voters

have received conﬂicting information about the candidates, in which case the third

voter can base her vote on all of the available information distributed through the

electorate, even though that distribution was not publicly known.

Exactly what are the information aggregation properties of various electoral

schemes is currently subject to much research. In some settings, the logic sketched

above can yield quite perverse results; for example, Ordeshook and Palfrey (1988)

provide an example in which an almost sure Condorcet winner (that is, an alternative

against which no alternative is preferred by a strict majority) is surely defeated in

an amendment agenda with incomplete information. And in other settings, it turns

¹⁴ Condorcet jury theorems address the problem of choosing one of two alternatives when voters are

uncertain about which is most in their interests. Typically, the theorems connect the size of the electorate

(jury) to the probability that majority voting outcomes coincide with the majority choice that would be

made under no uncertainty.